The below is one of the very first articles I ever posted here on Dean's World. I had to edit it slightly to close a grammatical hole I'd left open in the original piece, but it is basically unchanged and its logic remains as solid as ever. While it may seem silly to you, this one brainteaser really did change how I view most things. I confidently predict that most of you who read this and follow the logic carefully will be certain that I am wrong. Those of you think I am wrong will be irrefutably mistaken--as was I. This seems like a good week to resurrect the piece, which I have not re-posted in over two years.--Dean
If you go through life forming and sharing opinions, it is a rock-solid certainty that you will be wrong about something. The more opinions you have, the more that will happen. The bigger the issue, the more spectacularly wrong you're likely to be.
In my mid-20s, I stumbled on a brain teaser that, literally, changed how I viewed the world. As melodramatic as it sounds, I haven't been the same since. And, as with so many other things in this world, it's all Jerry Pournelle's fault....
None of us really likes to admit being wrong. One of the most seductive ways to avoid that is to change our opinions retroactively. We say, "No, no, you just misunderstood, you thought I was saying X when I really said Y." Or, even worse, sometimes we just stubbornly refuse to acknowledge the evidence in front of us.
Not that genuine misunderstandings don't happen. But a lot of people, when caught out as wrong, will say it didn't happen. Instead, they conveniently shift their position, but act like they didn't. It's almost as if we rewrite our memories, and by so doing rewrite the history of what we did or said. It's a pathology that's common to the human animal. Opinionated bloviators such as myself are particularly prone to the affliction. I don't claim to be cured, but I think I'm able to recognize the symptoms and, hopefully, manage the disease tolerably.
Silly as it seems, it was a brainteaser that woke me up to it. A brainteaser that not only showed me that I could be completely wrong, but rubbed my nose into my wrongness, repeatedly. Then I watched as some exceptionally intelligent people--mathematicians, engineers, people with various forms of Ph.D., Mensa members, and professional computer programmers also got it wrong, in astounding numbers.
Back in the early 1990s, I used to frequent the Jerry Pournelle RoundTable on the old GEnie network. Pournelle is well-known to old-time computer geeks for his "Computing at Chaos Manor" column in Byte magazine, and by Science Fiction fans for his many novels and short stories. He's also just about the smartest sumbitch I've ever met (I'm not even sure I needed to qualify that by saying "just about"). In his online forum, literally dozens of smart (and some not-so-smart) people would wile away endless hours discussing history, politics, religion, science, computers, books, guns and music. Gosh I loved it.
Anyway, one day one of the members of the RoundTable posted a simple brainteaser, related to a TV game show. It had appeared in Parade magazine, and where it came from before that I do not know. But here it is:
You find yourself on a game show called "Let's Make A Deal." The game is very simple. There are three doors: door #1, door #2, and door #3. Behind one door is a million dollars. The other two doors contain worthless joke prizes. All you have to do is pick which door you want to open, and you get whatever is behind it. But you only get to open one door. By simple math, then, you obviously have a 1 in 3 chance of picking the correct door and becoming an instant millionaire.
You pick a door. As soon as you tell Monty (the gameshow host) what door you want to open, he stops and says, "Now I'm going to do what we always do in this game. Now that you've made your choice, I'm going to open one of the other two doors for you, one with a booby prize." Then he does so. Then he asks, "Okay, now, would you like to stay with your original guess, or would you like to switch to the other door that's still closed? You only get one shot, so do you want to stay with your original choice, or switch?"
So here's the brainteaser: is there any compelling reason to switch doors?
To be clear, there is no trickery, and Monty is not cheating. Furthermore, the money has not moved, will not be moved, and if you open the right door, you win the cash. The money is either behind the door you first picked, or behind the remaining unopened door that Monty chose not to show you. Should you switch?
Think about that for a moment. To make it easier for you to avoid seeing the answer, I'll put some blank lines below for you to scroll through before seeing the answer:
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Logically speaking, this seems obvious to anyone with a sharp mind: you can switch if you want to, but it makes no difference. Monty has just eliminated one of your choices. Now you're down to two. You didn't know what was behind the doors before, and by opening one of them, you still don't know what's behind the other two. Your odds are 50/50 no matter which door you choose. So, switch or don't, it makes no difference.
Perfectly sensible, right? Absolutely. But the surprising answer is that you should switch doors.
I can tell that some of you are probably reading this and nodding--and then you're thinking to yourself, "No, that's not right. There really is no reason to switch. You can if you want to, or if you think there's cheating going on, but in a pure game, it's 50/50! You've gotten rid of one of the doors is all!"
I know this because it's the argument I made, and most people agreed with me. Dr. Pournelle himself saw it the same way. A stubborn few insisted that no, you really should switch. They were outnumbered and outgunned. It went on for a few days, with quite a few people joining the battle. Many of us were growing impatient with these clueless boobs who could not understand the logic. We explained it over and over: LOOK, you have only two choices! You had three but you eliminated one! You've only got two left! It's 50/50! You're letting yourself get confused by irrelevancies!
Then to my amazement, in the middle of writing a message explaining once again to the boobs why they were wrong, Dr. Pournelle said, "Oh my God, I can't believe I was so stupid!" and switched sides. Yes, you should go for the other door, he said.
I was stunned. As I say, I've always thought he was probably the smartest sumbitch I'd ever met. I'd tangled wits with him a few times, and usually (not always, but usually) came out on the losing side. I've often thought of him as one of my most important teachers--a sensei, a professor, a mensch. That was never formal, and I don't think he was quite aware of how I saw him. It's just that he had a disquieting knack for shaking me out of my comfortable prejudices, making me see things differently than I had before. And there he was, admitting he was wrong.
I and a few others spent two or three more days trying to convince everyone that they were crazy. Then I finally listened to what he and others were saying, and tried it empirically. When I did, I had to face it: I was wrong. It was not a matter of interpretation, and no pretending it didn't happen. I was simply wrong.
The difference between this and other brainteasers wasn't just that I couldn't figure it out. I'd often come across brainteasers I couldn't quite figure out, or that I got wrong. The difference here is that I was certain, damn-well certain that I was right. But I was wrong. Completely.
If you try it empirically, you'll find that if you stay with your original guess, you'll lose two times out of three. If you switch, you'll win two times out of three. By showing you an empty door after your first choice, Monty's given you information. Your original choice had only a 1 in 3 chance of being right. Odds were 2 to 1 that the money was behind one of the other two doors--and he just showed you which of the other two doors was empty.
Here's another way of thinking about it: let's play the same game, but it's got a thousand doors, not just three. Only one has money behind it. You pick the first door, and then Monty opens up 998 of the doors with junk prizes. Do you stay with your original, or do you switch? The odds of your first pick being right are 999-to-1 against, and that didn't change just because he opened up 998 empty doors.
Still don't believe me? I don't blame you. This puzzle popped up all over the online universe, and even made its way into magazines, newspapers, and newsletters. Wherever it went, most people gave the wrong answer. The Mensa monthly journal, for example, published an article claiming that the odds were only 50/50. A month later they printed a retraction. Mathematicians and others wrote to Parade and other publications swearing up and down that the odds were 50/50. It was quite something to watch, if you're enough of a geek to care about this sort of thing.
I also had several experiences where I related the puzzle to friends and co-workers, and they refused to believe you should switch. At several points, I tried placing wagers on it; challenging people to put money on the line usually made them wake up and try it empirically before risking their cash. But even then, I found that some people--smart people, quite often--stubbornly refused to take the bet. They merely insisted they "knew" they were right, and that was that.
It was when I encountered such people that I began to recognize a very human impulse. Sometimes, people will refuse to be change their minds once they've decided what to think. You can be friendly about it, joke about it, be irate or impatient about it, or try to present it any way you want: some people will not be convinced, and will even actively avoid looking at proof that they are wrong.
I also decided I didn't want to be one of those people.
(By the way, if still don't believe I'm right, shoot me an email, and we can set up the same wager. I'm so certain I'm right, I'm willing to gamble $cash$ that I can prove it to you. I'll pay up to $1,000 to anyone who can prove me wrong.)
Besides giving me insights into human behavior, this all emphasized something else to me: the world is not always a matter of opinion. You can't worm out of certain truths. 2+2 never equals 5. When someone you love dies, it's not debateable. If you love someone who doesn't love you back, you can't force the other person's feelings to change. Sexual congress between males and females tends to make babies.
More simply put: the world does not always conform itself to what we want it to be, or think it should be, or even what we are certain it must be. Some things are a matter of opinion or conjecture, but some things are stubborn, immutable facts. And cold, hard, ruthless facts contain the keys to finding whatever provable truths exist in the universe.
Maybe that all sounds obvious. But when you run smack into a circumstance where you are damn well convinced you're right but are wrong anyway, it shakes you up. I believe that whenever this happens, you're faced with three choices: backpeddle and pretend it never happened, stubbornly deny reality, or look the world right in the eye and say, "whoops." This entire experience made me decide to always strive to make that third choice.
It led me to start constantly testing whatever I believed. If I was going to express an opinion, it was going to be something I'd done my best to weigh against ruthless logic and cold, hard, empirically verifiable fact--or to the closest I could find to it. I also resolved to be willing to admit whenever I was not certain about something, or did not have enough information to form an opinion.
When you allow these beliefs to seep into your bones, when you consciously try to keep them in mind no matter where you are or what you're doing, it changes you. You find yourself never trusting 100% of anything you read or see. You wind up saying, "I have no opinion about that" or "that's what I think but I may be wrong" an awful lot. You wind up constantly facing the fact that the amount of things you know for certain are finite, but the things you don't know are infinite. If you keep it up, prejudices start to melt away. Sometimes you find yourself feeling just a little scared: "I have no idea what's going on" is a scary thing to admit.
On the other hand, it can be exhilirating. Because when you do pin down a fact, when you can verify something empirically, when you can demonstrate that 2+2=4 and there really is no arguing about it, my goodness it's powerful. It allows you to look someone right in the eye and say, "I believe that you are mistaken," even if you're talking to a doctor, a lawyer, a President, a politician, a priest, or any other expert who knows more than you about almost any subject. Because they can be wrong too, even on a matter where they generally know much more than you.
Facts are a marvelous levelling device, once you've got hold of one. Theories and logic be damned, a fact is a fact!
Frequently this sort of attitude will be mistaken for arrogance. This is because people commonly mistake confidence and certainty with arrogance. But confidence and certainty are what allowed us to do things like design bridges, put men on the moon, cure diseases, and create things like the internet. As long as your confidence and certainty is always tempered with, "Well, maybe I'm wrong, just show me where," you'll rarely go wrong.
All this forms the linchpin of my personal philosophy of life: the universe is knowable. Facts do exist and do not always conform themselves to our preconceptions or our wishes. When confronted with a fact that challenges your world view, it's your job to change your world view--at least, if you want to be an intellectually honest person. Living this way, you can be very certain about some things, not at all certain about others. Knowing which is which is the constant challenge.
But it's an infinitely rewarding challenge, if you take it seriously.
(And by the way, I still blame Pournelle for everything.)
